The matrix representation of the first cohomology of ${\mathfrak{gl}}_{0|2}$ with coefficients in the generalized Witt Lie superalgebra

Abstract

This paper is primarily concerned with the first cohomology of ${\mathfrak{gl}}_{0|2}$ with coefficients in the generalized Witt Lie superalgebra, where ${\mathfrak{gl}}_{0|2}$ is a subalgebra of the general linear Lie superalgebra. The derivations and inner derivations from ${\mathfrak{gl}}_{0|2}$ into submodules of the generalized Witt Lie superalgebra are represented by matrices, respectively. Then the first cohomology of ${\mathfrak{gl}}_{0|2}$ with coefficients in the generalized Witt Lie superalgebra is completely determined by matrices.

This paper has been withdrawn by the authors due to some paragraghs are unnecessarily lengthy and cumbrous